This study explores the efficacy of a Transformer model for 120-hour
streamflow prediction across 125 diverse locations in Iowa, US. Utilizing data
from the preceding 72 hours, including precipitation, evapotranspiration, and
discharge values, we developed a generalized model to predict future
streamflow. Our approach contrasts with traditional methods that typically rely
on location-specific models. We benchmarked the Transformer model's performance
against three deep learning models (LSTM, GRU, and Seq2Seq) and the Persistence
approach, employing Nash-Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency
(KGE), Pearson's r, and Normalized Root Mean Square Error (NRMSE) as metrics.
The study reveals the Transformer model's superior performance, maintaining
higher median NSE and KGE scores and exhibiting the lowest NRMSE values. This
indicates its capability to accurately simulate and predict streamflow,
adapting effectively to varying hydrological conditions and geographical
variances. Our findings underscore the Transformer model's potential as an
advanced tool in hydrological modeling, offering significant improvements over
traditional and contemporary approaches.

该研究探讨了 Transformer 模型在美国爱荷华州 125 个不同位置的 120 小时溪流预测中的有效性。利用前 72 小时的数据，包括降雨量、蒸发蒸腾量和流量值，我们开发了一个通用模型来预测未来的溪流流量。我们的方法与通常依赖于特定位置模型的传统方法相反。我们将 Transformer 模型的性能与三个深度学习模型（LSTM、GRU 和 Seq2Seq）以及持久性方法进行了基准测试，利用 Nash-Sutcliffe 效率（NSE）、Kling-Gupta 效度（KGE）、Pearson 相关系数和归一化均方根误差（NRMSE）作为度量标准。研究结果显示 Transformer 模型的卓越性能，具有更高的中位数 NSE 和 KGE 分数，并展现出最低的 NRMSE 值。这表明它能够准确模拟和预测溪流流量，并能有效适应不同的水文条件和地理变化。我们的发现强调了 Transformer 模型在水文建模中作为先进工具的潜力，相比传统和现代方法具有显著改进。

基于 Transformer 模型的广义水文预测：120 小时流量预测

Towards Generalized Hydrological Forecasting using Transformer Models  for 120-Hour Streamflow Prediction

Current hydrological modeling methods combine data-driven Machine Learning
(ML) algorithms and traditional physics-based models to address their
respective limitations incorrect parameter estimates from rigid physics-based
models and the neglect of physical process constraints by ML algorithms.
Despite the accuracy of ML in outcome prediction, the integration of scientific
knowledge is crucial for reliable predictions. This study introduces a Physics
Informed Machine Learning (PIML) model, which merges the process understanding
of conceptual hydrological models with the predictive efficiency of ML
algorithms. Applied to the Anandapur sub-catchment, the PIML model demonstrates
superior performance in forecasting monthly streamflow and actual
evapotranspiration over both standalone conceptual models and ML algorithms,
ensuring physical consistency of the outputs. This study replicates the
methodologies of Bhasme, P., Vagadiya, J., & Bhatia, U. (2022) from their
pivotal work on Physics Informed Machine Learning for hydrological processes,
utilizing their shared code and datasets to further explore the predictive
capabilities in hydrological modeling.

该研究介绍了一种物理信息驱动的机器学习（PIML）模型，将概念性水文模型的过程理解与机器学习算法的预测效能相结合，在安纳达普尔亚分水汇中应用，表明该模型在预测月流量和实际蒸散发方面的性能优于独立的概念模型和机器学习算法，确保输出的物理一致性。

复制研究：物理引导的机器学习增强水文模型

Replication Study: Enhancing Hydrological Modeling with Physics-Guided  Machine Learning

In many environmental applications, recurrent neural networks (RNNs) are
often used to model physical variables with long temporal dependencies.
However, due to mini-batch training, temporal relationships between training
segments within the batch (intra-batch) as well as between batches
(inter-batch) are not considered, which can lead to limited performance.
Stateful RNNs aim to address this issue by passing hidden states between
batches. Since Stateful RNNs ignore intra-batch temporal dependency, there
exists a trade-off between training stability and capturing temporal
dependency. In this paper, we provide a quantitative comparison of different
Stateful RNN modeling strategies, and propose two strategies to enforce both
intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by
defining a batch as a temporally ordered set of training segments, which
enables intra-batch sharing of temporal information. While this approach
significantly improves the performance, it leads to much larger training times
due to highly sequential training. To address this issue, we further propose a
new strategy which augments a training segment with an initial value of the
target variable from the timestep right before the starting of the training
segment. In other words, we provide an initial value of the target variable as
additional input so that the network can focus on learning changes relative to
that initial value. By using this strategy, samples can be passed in any order
(mini-batch training) which significantly reduces the training time while
maintaining the performance. In demonstrating our approach in hydrological
modeling, we observe that the most significant gains in predictive accuracy
occur when these methods are applied to state variables whose values change
more slowly, such as soil water and snowpack, rather than continuously moving
flux variables such as streamflow.

本文研究如何提高 RNN 模型在环境应用中的性能，主要通过对 Stateful RNN 模型策略的数量比较及两种依赖策略的提出来解决 batch 间（inter-batch）及 batch 内（intra-batch）的时间关联性问题，其中一种策略为将 batch 定义为时间上有序的一组训练片段从而促进 batch 内部时间信息的共享，另一种策略为在训练片段中增加目标变量的初始值以减少训练时间，该方法在水文模型中表现出显著的性能提升。